Here, is a known d-by-1 vector, is a d-by-1 vector to be identified, both and are known d-by-d matrix.

And I want to find the maximum value of L by taking the first order derivative with respect to .

Can anyone teach me how to take the first order derivative of this scalar with respect to a vector here?

Thanks a lot!!

Nov 10th 2010, 08:09 PM

xxp9

Note that both the denominator and the numerator are of the form of w'Aw, where w' is the transpose of w. Let f(w) = w'Aw, calcuate the differential like this:
Let t be a real number and x be a vector, then
f(w+tx) = (w'+tx')A(w+tx) = f(w) + tw'(A+A')x + o(t)
Thus the linear map df(x) = w'(A+A')x is the differental of f at the point w.